My cats like a cat bed I’ve bought them but there’s 1 bed for 3 cats, 2 of whom particularly like the bed.
I’ve narrowed down a list of cat beds that I think they might like. I’d ask them in purrson if I could but I don’t think they’d respond to pictures of cat beds.
Here’s the list but if you know any others that cats might like, please mention/link them:
It’s hard to say what they would like better but they’d probably like any of those (particularly ones that are like their own little cave).
I’d consider how much their human likes it (cost and how easy they are to clean).
My overlords/ladies like the design of the Love’s Cabin bed. There are two of them under the window next to my office chair. If I am in the office, both have occupants.
I’m sure they’ll like the shipping box better in any case. 
Can you not just get another of the one you know they like?
I have found that many cats like to sit on things that are close to the same color they are. So you might consider that in a purchase.
With all due respect, you have it exactly backward. Cats with white fur need to occupy black cushions, while black-furred cats must sit upon white. This maximizes the visibility of the hair they shed, and is an important part of being a successful cat.
Our two cats all but fight over this SmartyKat Deep Sleeper -
the loser either has to share or go sleep in one of the lesser cat beds (2 cats, 4 cat beds in our house, so you know who’s in charge 
)
As far as I can tell, they like it because it’s extremely deep, with high sides that provide comfort, but our cats don’t normally go for the cave route (2 of the other beds are caves/have a covered option). Probably because if you’re in a soft sided cat cave in my house, the other cat -IS- going to pounce on you while you’re sleeping in it.
Alternately, it’s because it is the most plush of the cat beds in the house, and perhaps they like the sort of thing. My cat → English translation skills sadly aren’t high enough to fully interpret their manifold whims.
The thing to consider with the tent or cave type of cat beds is they tend to like to sit on top of things, and or will play on them which then will squish them down. My two kittens did this with a really cute cat cave I got for them, which rendered it useless, as they never slept on top of the collapsed cave and couldn’t get inside of it. That said, there are some tent beds that have support rods made of plastic, which keeps them from collapsing. We’ve had one of those too.
I’ve always had success with the round-shaped beds, and I have one square-shaped bed too that they like as well. Some cats like to hide though, so they may prefer the cave or tent type of beds…it really depends on the personality and habits of your kitties.
Cardboard box with a sheepskin in it. Wood boxes work also.
Hmm, we found it amusing to see that our orange cat liked to sit on the reddish-brown chairs, and our black-white cat on the black&white hounds tooth couch. I honestly think they were looking for camouflage. I’ve seen other cats pick colors they blend into. I think it’s a real thing.
You might be right, for all I know. I was only joking. Of course, we humans will tend to notice the white-cat-on-dark or vice versa more, since we have the honor of dealing with the shedding.
My cat bed has a keyboard printed on it. They love it.
This is one of those questions for which there is no right answer. Cats only conform in their dedication to non-conformity. One of our cats prefers to sleep on a pillow on the foot of our bed while another sleeps between my legs. Another wants the heated pad.
Until the week they all decide to change preferences. Whether this is because the alpha decides to sleep somewhere else and everyone else adapts or something else is entirely between them.
I was Immy’s cat bed.